Washington (CNN)Republican senators reacted with outrage Tuesday after leaving a classified briefing about the murder of Washington Post journalist Jamal Khashoggi, promising swift action to confront both Saudi Arabia and the White House's timid response to the killing.

GOP Sens. Bob Corker of Tennessee and Lindsey Graham of South Carolina are leading the charge to offer new legislation that would rebuke Saudi Crown Prince Mohammed bin Salman, as well as potentially limit US involvement in the Saudi-led war in Yemen, saying their push was bolstered by the classified briefing, which detailed intelligence linking the Saudi leader to the murder of the US-based journalist.

"There's not a smoking gun, there's a smoking saw," said Graham, referring to reports that the Saudi team had included a forensic expert who arrived with equipment to dismember Khashoggi's body.

Referring to the prince, who is known by his initials, Graham said, "You have to be willfully blind not to come to the conclusion that this was orchestrated and organized by people under the command of MBS and that he was intrinsically involved in the demise of Mr. Khashoggi."

'Ordered, monitored'

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Corker added that the prince "ordered, monitored, the killing" of the father of four.

"If he were in front of a jury, he would be convicted of murder in about 30 minutes," Corker said.

The strong comments are the latest development in a controversy that has been building over the last two months as the Saudis have offered changing explanations about the disappearance and murder of Khashoggi at the Saudi Consulate in Istanbul on October 2.

Trump has made a concerted decision to avoid rebuking Saudi Arabia, claiming the kingdom's role in affecting global oil prices and its arms deals with the United States are more important to the national interest.

Trump, as well as Defense Secretary James Mattis and Secretary of State Mike Pompeo, have downplayed the crown prince's ties to the murder, with Pompeo saying there was no "direct evidence" linking him to Khashoggi's death.

No doubt, senators say

"Maybe he did and maybe he didn't," Trump said last month about whether the crown prince had known about the murder.

But senator after senator leaving the CIA briefing said there's no doubt that bin Salman was involved, adding that the United States cannot ignore the matter.

"Somebody should be punished," said Senate Appropriations Chairman Richard Shelby, a Republican from Alabama. "Now, the question is how do you separate the Saudi crown prince and his group from the nation itself? That might be the real policy question."

Indeed, after Haspel's briefing, the groundswell of certainty and disgust will likely complicate the administration's efforts to protect the prince and its relationship with Saudi Arabia, even as lawmakers have yet to coalesce around a legislative response.

'It's time'

Among the options: pull back from US involvement in the Saudi-led war in Yemen; deny any arms sales with Saudi Arabia; slap the crown prince with sanctions, along with a resolution saying the Senate finds him complicit in murder. How the legislative push gets resolved is uncertain, but the floor fight could begin as soon as Monday -- and put the administration on the defensive.

"It's time for the United States to be out of that war," said Sen. Chris Murphy, a Democrat Connecticut who co-sponsored a bipartisan resolution calling for an end to the US role in Yemen. "I know there are going to be a lot of efforts to try to remove the underlying language and replace it with something weaker. I don't think that ultimately saves lives in the way that the underlying bill does."

Corker said he's not certain he would support pulling back from Yemen but that "I deserve the right" to back a withdrawal of US involvement in the war effort.

"I don't want to do anything to harm our national interest, and I don't think that we've fully spoken to what the crown prince has done," Corker told CNN. "There are a lot of issues with Yemen that need to be addressed."

'Deep state' concerns

The CIA, meanwhile, is facing growing pressure to brief the full Senate, since Tuesday's briefing comprised only roughly a dozen senators from the party leadership and who sit on key committees.

Sen. Rand Paul, a Kentucky Republican, railed at the "deep state" for limiting the information flow to senators, while Senate Minority Leader Chuck Schumer demanded the full Senate be briefed as soon as possible.

"While I will not discuss the content of the Haspel briefing, it reinforced the need for a strong response to the murder of Jamal Khashoggi," the New York Democrat said. "CIA Director Haspel should brief the full Senate without delay."

Sen. Richard Durbin, an Illinois Democrat, said in a statement that "every Senator should hear what I heard this afternoon. CIA Director Haspel must brief the full Senate immediately."

And Sen. John Kennedy, a Louisiana Republican who was not part of the briefing, said that "by the director choosing to meet with some, but not others, congratulations to her, she has pissed off everybody."

High confidence

The office of Senate Majority Leader Mitch McConnell, a Kentucky Republican, has not responded to a request for comment on whether Haspel should brief the full chamber.

Haspel herself did not respond to CNN's questions as she left the briefing about whether it would satisfy senators' concerns.

The CIA had already concluded with high confidence that the prince was behind the murder, but senators said Haspel provided a much more fulsome briefing than the one they had gotten from Cabinet officials, including new evidence.

"Oh, there was much more information," Durbin said. "I went in believing the crown prince was directly responsible or at least complicit in this and my feeling was strengthened by the information."

'Yes'

Asked if the prince is responsible for Khashoggi's death, Durbin answered with one word: "Yes."

Graham said the United States should come down like a "ton of bricks" on the Saudis, adding that he can no longer do business with Saudi Arabia and "cannot support arm sales to Saudi Arabia" if the "crazy" crown prince is still running the country.

Some senators emphasized the need to find a balanced response. "We have to figure out a way to condemn the butchery and the murder in the strongest possible terms without blowing up the Middle East," Kennedy said. "That's what the Senate needs help on, and I am open to all suggestions on how to do that."

Others tried to downplay Haspel's briefing. Senate Majority Whip John Cornyn told CNN that Haspel should not come back and brief the whole Senate as senators on both sides have demanded.

"She didn't tell them anything that (Mattis and Pompeo didn't say)," the Texas Republican said, "so any senator who wants the information has had access to it."CNN's Annie Grayer, Clare Foran, Sarah Mucha, David Siegel and Zachary Cohen contributed to this report.